To graph the equation \( 1.50x + 0.50y = 20 \), you can follow these steps:
Step 1: Rewrite the equation in slope-intercept form (y = mx + b)
First, we want to solve for \( y \):
\[ 0.50y = 20 - 1.50x \]
Now divide everything by 0.50:
\[ y = -3x + 40 \]
Step 2: Identify the y-intercept and slope
From the equation \( y = -3x + 40 \):
- The slope (m) is -3.
- The y-intercept (b) is 40. This means that the line crosses the y-axis at the point (0, 40).
Step 3: Find another point on the line
To graph the line, you'll need at least two points. You can find a second point by substituting a value for \( x \).
For example, let's set \( x = 0 \): \[ y = -3(0) + 40 = 40 \quad \text{(already found)} \]
Now let's set \( x = 10 \): \[ y = -3(10) + 40 = -30 + 40 = 10 \] So another point is (10, 10).
Step 4: Plot the points and draw the line
- Plot the points (0, 40) and (10, 10) on a coordinate plane.
- Draw a straight line through those points, extending it in both directions.
Step 5: Add additional points (optional)
If you want to verify, you can calculate a few more points using different \( x \) values:
- For \( x = 20 \): \[ y = -3(20) + 40 = -60 + 40 = -20 \quad \text{(point: (20, -20))} \]
Plot the point (20, -20) as well.
Step 6: Finalize the graph
Make sure the line passes through all points plotted and label the axes and the equation of the line for clarity.
That's it! You now have the graph of the equation \( 1.50x + 0.50y = 20 \).